Answer to Question #297985 in Physics for ZEKE

Question

Two spherical objects have masses of 3.1 x 105 kg and 6.5 x 103 kg. The gravitational attraction between them is 65 N. How far apart are their centers?

Answer 1

Given:

$m_1=3.1*10^5\:\rm kg$

$m_2=6.5*10^3\:\rm kg$

$F=65\:\rm N$

The law of universal gravitation says

$$F=G\frac{m_1m_2}{r^2}$$

Thus

$$r=\sqrt{G\frac{m_1m_2}{F}}\\ =\sqrt{6.67*10^{-11}\frac{3.1*10^5*6.5*10^3}{65}}=0.045\:\rm m$$